Finite Group Databasebeta

← #33052175

Subgroups — #33052175

Order 18688.

1046 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989261C211yesmaximal, characteristic
2#22618589C211yesmaximal, characteristic, complemented
3#22608301C211yesmaximal, characteristic, complemented
4#22608298C211yesmaximal, characteristic, complemented
5#22608284C211yesmaximal, characteristic, complemented
6#22608282C211yesmaximal, characteristic, complemented
7#22608280C211yesmaximal, characteristic, complemented
8#22608277C211yesmaximal, characteristic, complemented
9#22608271C211yesmaximal, characteristic, complemented
10#22608263C211yesmaximal, characteristic, complemented
11#22608257C211yesmaximal, characteristic, complemented
12#22608251C211yesmaximal, characteristic, complemented
13#22608243C211yesmaximal, characteristic, complemented
14C2×#17988310C211yesmaximal, characteristic, complemented
15C73×#2924C211yesmaximal, characteristic, complemented
16#17989261—21no—
17#17989261—21no—
18#17989261—21no—
19#17989261—21no—
20#17989261—21no—
21#17989261—21no—
22#17989261—21no—
23#17989261—21no—
24C2×#14556586C411yescharacteristic
25C2×#14556585C2211yescharacteristic
26C2×#14556579C2211yescharacteristic
27C2×#14556576C411yescharacteristic
28C2×#14556576C411yescharacteristic
29C2×#14556574C2211yescharacteristic
30C2×#14556569C411yescharacteristic
31C2×#14556568C411yescharacteristic
32C2×#14556561C411yescharacteristic
33C2×C4×D292C2211yescharacteristic
34C2×#14556551C411yescharacteristic
35C2×#14556548C2211yescharacteristic
36C22×#11924005C2211yescharacteristic
37C2×C22⋊C4×D73C411yescharacteristic
38#17988648—21no—
39#17988648—21no—
40#17988644C2211yescharacteristic, complemented
41#17988644C2211yescharacteristic, complemented
42#17988640C2211yescharacteristic, complemented
43#17988640C2211yescharacteristic, complemented
44#17988614—21no—
45#17988551C2211yescharacteristic
46C2×C22⋊#10596831C2211yescharacteristic
47#17988543—21no—
48#17988312C2211yescharacteristic, complemented
49#17988312C2211yescharacteristic, complemented
50#17988312C2211yescharacteristic, complemented
51#17988312C2211yescharacteristic, complemented
52#17988310C2211yescharacteristic
53#17988310C2211yescharacteristic
54#17988310C2211yescharacteristic
55#17988310C2211yescharacteristic
56#17988310C2211yescharacteristic
57#17988310C2211yescharacteristic
58#17988310C2211yescharacteristic
59#17988310C2211yescharacteristic
60#17988310C2211yescharacteristic, complemented
61#17988310C2211yescharacteristic, complemented
62#17988310C2211yescharacteristic, complemented
63#17988310C2211yescharacteristic, complemented
64C2×#117×C73C2211yescharacteristic
65#433×C73—21no—
66#433×C73—21no—
67#432×C73C2211yescharacteristic, complemented
68#432×C73C2211yescharacteristic, complemented
69#431×C73C2211yescharacteristic, complemented
70#431×C73C2211yescharacteristic, complemented
71#424×C73—21no—
72#407×C73C2211yescharacteristic
73C2×C22⋊C8×C73C2211yescharacteristic
74#405×C73—21no—
75C24×D73C2×C411yescharacteristic
76C22×Dic146C2×C411yescharacteristic
77C22×D292C2×C411yescharacteristic
78C22×D292C2×C411yescharacteristic
79C22×C22⋊D73C2×C411yescharacteristic
80C23×Dic73C2×C411yescharacteristic
81C22×C4×D73C2×C411yescharacteristic
82C22×C4×D73C2×C411yescharacteristic
83C22×C4×D73C2×C411yescharacteristic
84C2×#11924012—21no—
85C22×#10596831—21no—
86#14556586—21no—
87#14556586—21no—
88#14556586—21no—
89#14556586—21no—
90#14556585—21no—
91#14556585—21no—
92#14556585—21no—
93#14556585—21no—
94#14556579—21no—
95#14556579—21no—
96#14556579—21no—
97#14556579—21no—
98#14556576—21no—
99#14556576—21no—
100#14556576—21no—
101#14556576—21no—
102#14556576—21no—
103#14556576—21no—
104#14556576—21no—
105#14556576—21no—
106#14556574—21no—
107#14556574—21no—
108#14556574—21no—
109#14556574—21no—
110#14556569—21no—
111#14556569—21no—
112#14556569—21no—
113#14556569—21no—
114#14556568—21no—
115#14556568—21no—
116#14556568—21no—
117#14556568—21no—
118#14556561—21no—
119#14556561—21no—
120#14556561—21no—
121#14556561—21no—
122C4×D292—21no—
123C4×D292—21no—
124C4×D292—21no—
125C4×D292—21no—
126#14556551—21no—
127#14556551—21no—
128#14556551—21no—
129#14556551—21no—
130#14556548—21no—
131#14556548—21no—
132#14556548—21no—
133#14556548—21no—
134C2×C4⋊Dic73C2×C411yescharacteristic
135C2×#11924007C2×C411yescharacteristic
136C2×#11924007C2×C411yescharacteristic
137C2×#11924007C2×C411yescharacteristic
138C2×#11924007C2×C411yescharacteristic
139C2×#11924007C2311yescharacteristic
140C2×C22⋊Dic73C2×C411yescharacteristic
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005C2×C411yescharacteristic
146C2×#11924005C2×C411yescharacteristic
147C2×#11924005C2×C411yescharacteristic
148C2×#11924005C2×C411yescharacteristic
149C2×#11924005C2×C411yescharacteristic
150C2×#11924005C2×C411yescharacteristic
151C2×#11924005C2×C411yescharacteristic
152C2×#11924005C2×C411yescharacteristic
153C2×#11924005C2311yescharacteristic
154C2×#11924005C2311yescharacteristic
155C2×#11924005C2311yescharacteristic
156C22⋊C4×D73—21no—
157C22⋊C4×D73—21no—
158C22⋊C4×D73—21no—
159C22⋊C4×D73—21no—
160C2×C4×Dic73C2×C411yescharacteristic
161C4⋊#10596831—21no—
162C4⋊#10596831—21no—
163C4⋊#10596831—21no—
164C4⋊#10596831—21no—
165C22⋊#10596831—21no—
166C22⋊#10596831—21no—
167C22⋊#10596831C2311yescharacteristic
168C22⋊#10596831C2311yescharacteristic
169C22⋊#10596831C2311yescharacteristic
170C22⋊#10596831C2311yescharacteristic
171#14556502—21no—
172#14556502—21no—
173C4×#10596831—21no—
174C4×#10596831—21no—
175C23×C4×C73C2311yescharacteristic
176C2×M16×C73—21no—
177C22×C8×C73—21no—
178#117×C73D411yescharacteristic
179#117×C73D411yescharacteristic
180#117×C73D411yescharacteristic
181#117×C73D411yescharacteristic
182#117×C73D411yescharacteristic
183#117×C73D411yescharacteristic
184#117×C73D411yescharacteristic
185#117×C73D411yescharacteristic
186C2×C4⋊C4×C73C2×C411yescharacteristic
187C2×C4⋊C4×C73C2×C411yescharacteristic
188C2×C22⋊C4×C73C2×C411yescharacteristic
189C2×C22⋊C4×C73C2×C411yescharacteristic
190C2×C42×C73C2311yescharacteristic
191C2×C42×C73C2311yescharacteristic
192C4⋊C8×C73—21no—
193C4⋊C8×C73—21no—
194C4⋊C8×C73—21no—
195C4⋊C8×C73—21no—
196C22⋊C8×C73—21no—
197C22⋊C8×C73—21no—
198C22⋊C8×C73C2311yescharacteristic
199C22⋊C8×C73C2311yescharacteristic
200C22⋊C8×C73C2311yescharacteristic
201C22⋊C8×C73C2311yescharacteristic
202#97×C73—21no—
203#97×C73—21no—
204C4×C8×C73—21no—
205C4×C8×C73—21no—
206C23×D73—21no—
207C23×D73—21no—
208C23×D73—22no—
209C23×D73—41no—
210C23×D73—42no—
211C23×D73—81no—
212C23×D73C22×C411yescharacteristic
213C23×D73C22×C411yescharacteristic
214C23×D73C22×C411yescharacteristic
215C2×Dic146—21no—
216C2×Dic146—21no—
217C2×Dic146—81no—
218C2×D292—22no—
219C2×D292—21no—
220C2×D292—21no—
221C2×D292—21no—
222C2×D292—21no—
223C2×D292—41no—
224C2×D292—81no—
225C2×C22⋊D73—21no—
226C2×C22⋊D73—21no—
227C2×C22⋊D73—42no—
228C22×Dic73—21no—
229C22×Dic73—21no—
230C22×Dic73—81no—
231C22×Dic73C22×C411yescharacteristic
232C22×Dic73C22×C411yescharacteristic
233C22×Dic73C22×C411yescharacteristic
234C22×Dic73C22×C411yescharacteristic
235C22×Dic73C22×C411yescharacteristic
236C2×C4×D73—22no—
237C2×C4×D73—21no—
238C2×C4×D73—21no—
239C2×C4×D73—21no—
240C2×C4×D73—21no—
241C2×C4×D73—21no—
242C2×C4×D73—21no—
243C2×C4×D73—41no—
244C2×C4×D73—81no—
245C2×C4×D73—81no—
246#11924012—42no—
247C2×#10596831—21no—
248C2×#10596831—21no—
249C2×#10596831—21no—
250C2×#10596831—21no—
251C2×#10596831—42no—
252C4⋊Dic73—21no—
253C4⋊Dic73—21no—
254#11924007—21no—
255#11924007—21no—
256#11924007—21no—
257#11924007—21no—
258#11924007—21no—
259#11924007—21no—
260#11924007—21no—
261#11924007—21no—
262#11924007—21no—
263#11924007—21no—
264C22⋊Dic73—21no—
265C22⋊Dic73—21no—
266#11924005—21no—
267#11924005—21no—
268#11924005—21no—
269#11924005—21no—
270#11924005—21no—
271#11924005—21no—
272#11924005—21no—
273#11924005—21no—
274#11924005—21no—
275#11924005—21no—
276#11924005—21no—
277#11924005—21no—
278#11924005—21no—
279#11924005—21no—
280#11924005—21no—
281#11924005—21no—
282#11924005—21no—
283#11924005—21no—
284#11924005—21no—
285#11924005—21no—
286#11924005—21no—
287#11924005—21no—
288C4×Dic73—21no—
289C4×Dic73—21no—
290C24×C73C22×C411yescharacteristic
291C22×C4×C73—42no—
292C22×C4×C73C22×C411yescharacteristic
293C22×C4×C73C22×C411yescharacteristic
294C22×C4×C73C22×C411yescharacteristic
295C22×C4×C73C22×C411yescharacteristic
296C22×C4×C73C22×C411yescharacteristic
297C22×C4×C73C2×D411yescharacteristic
298C22×C4×C73C2×D411yescharacteristic
299C22×C4×C73C2×D411yescharacteristic
300C22×C4×C73C2×D411yescharacteristic
301C22×C4×C73C2411yescharacteristic
302M16×C73—42no—
303C2×C8×C73—21no—
304C2×C8×C73—21no—
305C2×C8×C73—21no—
306C2×C8×C73—21no—
307C2×C8×C73—42no—
308C4⋊C4×C73C22⋊C411yescharacteristic
309C4⋊C4×C73C22⋊C411yescharacteristic
310C4⋊C4×C73C22⋊C411yescharacteristic
311C4⋊C4×C73C22⋊C411yescharacteristic
312C4⋊C4×C73C22⋊C411yescharacteristic
313C4⋊C4×C73C22⋊C411yescharacteristic
314C4⋊C4×C73C22⋊C411yescharacteristic
315C4⋊C4×C73C22⋊C411yescharacteristic
316C22⋊C4×C73C22⋊C411yescharacteristic
317C22⋊C4×C73C22⋊C411yescharacteristic
318C22⋊C4×C73C22⋊C411yescharacteristic
319C22⋊C4×C73C22⋊C411yescharacteristic
320C22⋊C4×C73C22⋊C411yescharacteristic
321C22⋊C4×C73C22⋊C411yescharacteristic
322C22⋊C4×C73C22⋊C411yescharacteristic
323C22⋊C4×C73C22⋊C411yescharacteristic
324C42×C73C2×D411yescharacteristic
325C42×C73C2×D411yescharacteristic
326C42×C73C2×D411yescharacteristic
327C42×C73C2×D411yescharacteristic
328C42×C73C2×D411yescharacteristic
329C42×C73C2×D411yescharacteristic
330C42×C73C2×D411yescharacteristic
331C42×C73C2×D411yescharacteristic
332C23×C73—21no—
333C23×C73—21no—
334C23×C73—22no—
335C23×C73—41no—
336C23×C73C2×C22⋊C411yescharacteristic
337C23×C73C2×C22⋊C411yescharacteristic
338C23×C73C23×C411yescharacteristic
339C22×D73—21no—
340C22×D73—21no—
341C22×D73—21no—
342C22×D73—21no—
343C22×D73—21no—
344C22×D73—21no—
345C22×D73—21no—
346C22×D73—21no—
347C22×D73—42no—
348C22×D73—42no—
349C22×D73—41no—
350C22×D73—41no—
351C22×D73—42no—
352C22×D73—42no—
353C22×D73—41no—
354C22×D73—41no—
355C22×D73—41no—
356C22×D73—41no—
357C22×D73—81no—
358C22×D73—81no—
359C22×D73—84no—
360C22×D73—84no—
361C22×D73#13112yes—
362C2×C4×C73—21no—
363C2×C4×C73—21no—
364C2×C4×C73—21no—
365C2×C4×C73—21no—
366C2×C4×C73—22no—
367C2×C4×C73—22no—
368C2×C4×C73—41no—
369C2×C4×C73—41no—
370C2×C4×C73—41no—
371C2×C4×C73—41no—
372C2×C4×C73—41no—
373C2×C4×C73—41no—
374C2×C4×C73C2×C22⋊C411yescharacteristic
375C2×C4×C73C2×C22⋊C411yescharacteristic
376C2×C4×C73C2×C22⋊C411yescharacteristic
377C2×C4×C73C2×C22⋊C411yescharacteristic
378C2×C4×C73C2×C22⋊C411yescharacteristic
379C2×C4×C73C2×C22⋊C411yescharacteristic
380C2×C4×C73C2×C22⋊C411yescharacteristic
381C2×C4×C73C2×C22⋊C411yescharacteristic
382C2×C4×C73C2×C22⋊C411yescharacteristic
383C2×C4×C73C2×C22⋊C411yescharacteristic
384C2×C4×C73C22×D411yescharacteristic
385C2×C4×C73C22×D411yescharacteristic
386C22⋊D73—42no—
387C22⋊D73—42no—
388C2×Dic73—21no—
389C2×Dic73—21no—
390C2×Dic73—21no—
391C2×Dic73—21no—
392C2×Dic73—21no—
393C2×Dic73—21no—
394C2×Dic73—21no—
395C2×Dic73—41no—
396C2×Dic73—41no—
397C2×Dic73—41no—
398C2×Dic73—41no—
399C2×Dic73—81no—
400C2×Dic73—81no—
401D292—42no—
402D292—42no—
403D292—81no—
404D292—81no—
405C4×D73—42no—
406C4×D73—42no—
407C4×D73—81no—
408C4×D73—81no—
409C4×D73—81no—
410C4×D73—81no—
411Dic146—81no—
412Dic146—81no—
413C8×C73—41no—
414C8×C73—41no—
415C8×C73—41no—
416C8×C73—41no—
417#10596831—41no—
418#10596831—41no—
419#10596831—41no—
420#10596831—41no—
421C22×C73—21no—
422C22×C73—21no—
423C22×C73—21no—
424C22×C73—21no—
425C22×C73—21no—
426C22×C73—21no—
427C22×C73—21no—
428C22×C73—42no—
429C22×C73—42no—
430C22×C73#41012yes—
431C22×C73C22×C22⋊C411yescharacteristic
432C22×C73C2×#13111yescharacteristic
433C22×C73#56811yescharacteristic
434C2×D73—22no—
435C2×D73—42no—
436C2×D73—41no—
437C2×D73—41no—
438C2×D73—42no—
439C2×D73—41no—
440C2×D73—41no—
441C2×D73—41no—
442C2×D73—41no—
443C2×D73—41no—
444C2×D73—41no—
445C2×D73—84no—
446C2×D73—84no—
447C2×D73—81no—
448C2×D73—81no—
449C2×D73—81no—
450C2×D73—81no—
451C4×C73—21no—
452C4×C73—21no—
453C4×C73—21no—
454C4×C73—21no—
455C4×C73—21no—
456C4×C73—21no—
457C4×C73—21no—
458C4×C73—21no—
459C4×C73—21no—
460C4×C73—21no—
461C4×C73—21no—
462C4×C73—21no—
463Dic73—41no—
464Dic73—41no—
465Dic73—41no—
466Dic73—41no—
467Dic73—41no—
468#17412—731nomaximal, Sylow
469C2×C73—21no—
470C2×C73—21no—
471C2×C73—22no—
472C2×C73—41no—
473C2×C73#288011yescharacteristic
474C2×C73C2×#41011yescharacteristic
475C2×C73#288811yescharacteristic
476D73—42no—
477D73—81no—
478D73—81no—
479C2×#551—731no—
480#2924—731no—
481#2924D7311yescharacteristic, complemented
482#1473—731no—
483#1473—731no—
484#1469—731no—
485#1469—731no—
486#1468—731no—
487#1468—731no—
488#1466—731no—
489#1464—731no—
490#1462—731no—
491#1460—731no—
492#1458—731no—
493C2×#323—731no—
494C73#1741211yescharacteristic, complemented, Sylow
495#551—1461no—
496#551—1461no—
497#551—1461no—
498#551—1461no—
499#551—1461no—
500#551—1461no—
501#551—1461no—
502#551—1461no—
503C2×#126—731no—
504C2×#126—731no—
505C2×#124—731no—
506C2×#123—731no—
507C2×#123—731no—
508C2×#123—731no—
509C2×C22⋊Q8—731no—
510C2×C22⋊Q8—731no—
511C2×#120—731no—
512C2×C4×D4—731no—
513C2×C4×D4—731no—
514C2×#117—731no—
515C2×#117C2×D7311yescharacteristic
516C22×C22⋊C4—731no—
517C22×C22⋊C4—731no—
518#433—21no—
519#433—21no—
520#433—1461no—
521#433—1461no—
522#432—731no—
523#432—731no—
524#432C2×D7311yescharacteristic, complemented
525#432C2×D7311yescharacteristic, complemented
526#431—731no—
527#431—731no—
528#431C2×D7311yescharacteristic, complemented
529#431C2×D7311yescharacteristic, complemented
530#424—21no—
531#424—1461no—
532#407—731no—
533#407C2×D7311yescharacteristic
534C2×C22⋊C8—731no—
535C2×C22⋊C8C2×D7311yescharacteristic
536#405—21no—
537#405—1461no—
538#324—731no—
539#324—731no—
540#324—731no—
541#324—731no—
542#323—731no—
543#323—731no—
544#323—731no—
545#323—731no—
546#323—731no—
547#323—731no—
548#323—731no—
549#323—731no—
550#323—731no—
551#323—731no—
552#323—731no—
553#323—731no—
554C25—731no—
555C22×Q8—731no—
556C22×D4—731no—
557C22×D4—731no—
558C22×D4—731no—
559C23×C4—731no—
560C23×C4—731no—
561C23×C4—731no—
562C23×C4—731no—
563C23×C4C22×D7311yescharacteristic
564C2×M16—21no—
565C2×M16—1461no—
566C22×C8—21no—
567C22×C8—1461no—
568#126—1461no—
569#126—1461no—
570#126—1461no—
571#126—1461no—
572#126—1461no—
573#126—1461no—
574#126—1461no—
575#126—1461no—
576#124—1461no—
577#124—1461no—
578#124—1461no—
579#124—1461no—
580#123—1461no—
581#123—1461no—
582#123—1461no—
583#123—1461no—
584#123—1461no—
585#123—1461no—
586#123—1461no—
587#123—1461no—
588#123—1461no—
589#123—1461no—
590#123—1461no—
591#123—1461no—
592C22⋊Q8—1461no—
593C22⋊Q8—1461no—
594C22⋊Q8—1461no—
595C22⋊Q8—1461no—
596C22⋊Q8—1461no—
597C22⋊Q8—1461no—
598C22⋊Q8—1461no—
599C22⋊Q8—1461no—
600#120—1461no—
601#120—1461no—
602#120—1461no—
603#120—1461no—
604C4×D4—1461no—
605C4×D4—1461no—
606C4×D4—1461no—
607C4×D4—1461no—
608C4×D4—1461no—
609C4×D4—1461no—
610C4×D4—1461no—
611C4×D4—1461no—
612#117—1461no—
613#117—1461no—
614#117—1461no—
615#117—1461no—
616#117D29211yescharacteristic
617#117D29211yescharacteristic
618#117D29211yescharacteristic
619#117D29211yescharacteristic
620#117C22⋊D7311yescharacteristic
621#117C22⋊D7311yescharacteristic
622#117C22⋊D7311yescharacteristic
623#117C22⋊D7311yescharacteristic
624C2×C4⋊C4—731no—
625C2×C4⋊C4—731no—
626C2×C4⋊C4—731no—
627C2×C4⋊C4—731no—
628C2×C4⋊C4—731no—
629C2×C4⋊C4—731no—
630C2×C4⋊C4C4×D7311yescharacteristic
631C2×C4⋊C4C4×D7311yescharacteristic
632C2×C22⋊C4—731no—
633C2×C22⋊C4—731no—
634C2×C22⋊C4—731no—
635C2×C22⋊C4—731no—
636C2×C22⋊C4—731no—
637C2×C22⋊C4—731no—
638C2×C22⋊C4—731no—
639C2×C22⋊C4—731no—
640C2×C22⋊C4—731no—
641C2×C22⋊C4—731no—
642C2×C22⋊C4—731no—
643C2×C22⋊C4—731no—
644C2×C22⋊C4—1461no—
645C2×C22⋊C4—1461no—
646C2×C22⋊C4—1461no—
647C2×C22⋊C4—1461no—
648C2×C22⋊C4—1461no—
649C2×C22⋊C4—1461no—
650C2×C22⋊C4—1461no—
651C2×C22⋊C4—1461no—
652C2×C22⋊C4C4×D7311yescharacteristic
653C2×C22⋊C4C4×D7311yescharacteristic
654C2×C42—731no—
655C2×C42C22×D7311yescharacteristic
656C2×C42C22×D7311yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—21no—
660C4⋊C8—21no—
661C4⋊C8—1461no—
662C4⋊C8—1461no—
663C4⋊C8—1461no—
664C4⋊C8—1461no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—731no—
668C22⋊C8—731no—
669C22⋊C8—731no—
670C22⋊C8—731no—
671C22⋊C8—1461no—
672C22⋊C8—1461no—
673C22⋊C8C22×D7311yescharacteristic
674C22⋊C8C22×D7311yescharacteristic
675C22⋊C8C22×D7311yescharacteristic
676C22⋊C8C22×D7311yescharacteristic
677#97—21no—
678#97—21no—
679#97—1461no—
680#97—1461no—
681C4×C8—21no—
682C4×C8—21no—
683C4×C8—1461no—
684C4×C8—1461no—
685C24—2922no—
686C24—2921no—
687C24—5841no—
688C24—731no—
689C24—731no—
690C24—731no—
691C24—1462no—
692C24—1461no—
693C24—1461no—
694C24C2×C4×D7311yescharacteristic
695C2×Q8—5841no—
696C2×Q8—1461no—
697C2×Q8—1461no—
698C2×D4—2921no—
699C2×D4—2922no—
700C2×D4—5841no—
701C2×D4—1462no—
702C2×D4—1461no—
703C2×D4—1461no—
704C2×D4—1461no—
705C2×D4—1461no—
706C2×D4—1461no—
707C2×D4—1461no—
708C22×C4—42no—
709C22×C4—2921no—
710C22×C4—5841no—
711C22×C4—5841no—
712C22×C4—5841no—
713C22×C4—731no—
714C22×C4—731no—
715C22×C4—731no—
716C22×C4—731no—
717C22×C4—731no—
718C22×C4—1462no—
719C22×C4—1461no—
720C22×C4—1461no—
721C22×C4—1461no—
722C22×C4—1461no—
723C22×C4—1461no—
724C22×C4—1461no—
725C22×C4—1461no—
726C22×C4—1461no—
727C22×C4C2×C4×D7311yescharacteristic
728C22×C4C2×C4×D7311yescharacteristic
729C22×C4C2×C4×D7311yescharacteristic
730C22×C4C2×C4×D7311yescharacteristic
731C22×C4C2×C4×D7311yescharacteristic
732C22×C4C2×C22⋊D7311yescharacteristic
733C22×C4C2×C22⋊D7311yescharacteristic
734C22×C4C2×D29211yescharacteristic
735C22×C4C2×D29211yescharacteristic
736C22×C4C23×D7311yescharacteristic
737M16—42no—
738M16—2922no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—42no—
744C2×C8—2922no—
745C2×C8—1461no—
746C2×C8—1461no—
747C2×C8—1461no—
748C2×C8—1461no—
749C4⋊C4—1461no—
750C4⋊C4—1461no—
751C4⋊C4—1461no—
752C4⋊C4—1461no—
753C4⋊C4—1461no—
754C4⋊C4—1461no—
755C4⋊C4—1461no—
756C4⋊C4—1461no—
757C4⋊C4—1461no—
758C4⋊C4—1461no—
759C4⋊C4—1461no—
760C4⋊C4—1461no—
761C4⋊C4#1192400511yescharacteristic
762C4⋊C4#1192400511yescharacteristic
763C4⋊C4#1192400511yescharacteristic
764C4⋊C4#1192400511yescharacteristic
765C4⋊C4#1192400511yescharacteristic
766C4⋊C4#1192400511yescharacteristic
767C4⋊C4#1192400511yescharacteristic
768C4⋊C4#1192400511yescharacteristic
769C22⋊C4—1461no—
770C22⋊C4—1461no—
771C22⋊C4—1461no—
772C22⋊C4—1461no—
773C22⋊C4—1461no—
774C22⋊C4—1461no—
775C22⋊C4—1461no—
776C22⋊C4—1461no—
777C22⋊C4—1461no—
778C22⋊C4—1461no—
779C22⋊C4—1461no—
780C22⋊C4—1461no—
781C22⋊C4—1461no—
782C22⋊C4—1461no—
783C22⋊C4—1461no—
784C22⋊C4—1461no—
785C22⋊C4—1461no—
786C22⋊C4—1461no—
787C22⋊C4—1461no—
788C22⋊C4—1461no—
789C22⋊C4—1461no—
790C22⋊C4—1461no—
791C22⋊C4—1461no—
792C22⋊C4—1461no—
793C22⋊C4#1192400511yescharacteristic
794C22⋊C4#1192400511yescharacteristic
795C22⋊C4#1192400511yescharacteristic
796C22⋊C4#1192400511yescharacteristic
797C22⋊C4#1192400511yescharacteristic
798C22⋊C4#1192400511yescharacteristic
799C22⋊C4#1192400511yescharacteristic
800C22⋊C4#1192400511yescharacteristic
801C42—1461no—
802C42—1461no—
803C42C2×C22⋊D7311yescharacteristic
804C42C2×C22⋊D7311yescharacteristic
805C42C2×C22⋊D7311yescharacteristic
806C42C2×C22⋊D7311yescharacteristic
807C42C2×D29211yescharacteristic
808C42C2×D29211yescharacteristic
809C42C2×D29211yescharacteristic
810C42C2×D29211yescharacteristic
811C23—22no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—2921no—
816C23—2921no—
817C23—2922no—
818C23—2921no—
819C23—2921no—
820C23—2921no—
821C23—2921no—
822C23—2922no—
823C23—2922no—
824C23—2922no—
825C23—5841no—
826C23—5841no—
827C23—5844no—
828C23—5844no—
829C23—732no—
830C23—1461no—
831C23—1461no—
832C23—1461no—
833C23—1461no—
834C23—1461no—
835C23—1461no—
836C23—1461no—
837C23—1461no—
838C23C2×#1192400511yescharacteristic
839C23C2×#1192400511yescharacteristic
840C23C22×C4×D7311yescharacteristic
841Q8—5841no—
842Q8—5841no—
843D4—2922no—
844D4—2922no—
845D4—2922no—
846D4—2922no—
847D4—5841no—
848D4—5841no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—2922no—
862C2×C4—2922no—
863C2×C4—2921no—
864C2×C4—2921no—
865C2×C4—2921no—
866C2×C4—2921no—
867C2×C4—5841no—
868C2×C4—5841no—
869C2×C4—5841no—
870C2×C4—5841no—
871C2×C4—5841no—
872C2×C4—5841no—
873C2×C4—1461no—
874C2×C4—1461no—
875C2×C4—1461no—
876C2×C4—1461no—
877C2×C4—1461no—
878C2×C4—1461no—
879C2×C4—1461no—
880C2×C4C2×#1192400511yescharacteristic
881C2×C4C2×#1192400511yescharacteristic
882C2×C4C2×#1192400511yescharacteristic
883C2×C4C2×#1192400511yescharacteristic
884C2×C4C2×#1192400511yescharacteristic
885C2×C4C2×#1192400511yescharacteristic
886C2×C4C2×#1192400511yescharacteristic
887C2×C4C2×#1192400511yescharacteristic
888C2×C4C2×#1192400511yescharacteristic
889C2×C4C2×#1192400511yescharacteristic
890C2×C4C22×C22⋊D7311yescharacteristic
891C2×C4C22×D29211yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C8—2921no—
897C8—2921no—
898C8—2921no—
899C8—2921no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—42no—
908C22—42no—
909C22—2922no—
910C22—2922no—
911C22—2921no—
912C22—2921no—
913C22—2921no—
914C22—2921no—
915C22—2921no—
916C22—2921no—
917C22—2921no—
918C22—2921no—
919C22—5844no—
920C22—5841no—
921C22—5841no—
922C22—5841no—
923C22—5841no—
924C22—5844no—
925C22—1462no—
926C22#1798856012yes—
927C22C22×#1192400511yescharacteristic
928C22#131×D7311yescharacteristic
929C22#1798935211yescharacteristic
930C4—21no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—2921no—
943C4—2921no—
944C4—2921no—
945C4—2921no—
946C4—2921no—
947C2—21no—
948C2—21no—
949C2—22no—
950C2—41no—
951C2—2922no—
952C2—5841no—
953C2—5841no—
954C2#2261837811yescharacteristic
955C2C2×#1798856011yescharacteristic
956C2#2261840911yescharacteristic
subgroupG/H
centerC22C22×#11924005
commutatorC23×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2924C2
socleC22×C73C22×C22⋊C4
prime radicalC2×#14556561C4
cosocleC22×C4×C73C24
hypercenter#2924D73
hypocenterC73#17412
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22618589C2semidirect
3. #22608301C2semidirect
4. #22608298C2semidirect
5. #22608284C2semidirect
6. #22608282C2semidirect
7. #22608280C2semidirect
8. #22608277C2semidirect
9. #22608271C2semidirect
10. #22608263C2semidirect
11. #22608257C2semidirect
12. #22608251C2semidirect
13. #22608243C2semidirect
14. C2×#17988310C2semidirect
15. C73×#2924C2semidirect
40. #17988644C22semidirect
41. #17988644C22semidirect
42. #17988640C22semidirect
43. #17988640C22semidirect
48. #17988312C22semidirect
49. #17988312C22semidirect
50. #17988312C22semidirect
51. #17988312C22semidirect
60. #17988310C22semidirect
61. #17988310C22semidirect
62. #17988310C22semidirect
63. #17988310C22semidirect
67. #432×C73C22semidirect
68. #432×C73C22semidirect
69. #431×C73C22semidirect
70. #431×C73C22semidirect
481. #2924D73semidirect
494. C73#17412semidirect
524. #432C2×D73semidirect
525. #432C2×D73semidirect
528. #431C2×D73semidirect
529. #431C2×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179892612
#226185892
#226083012
#226082982
#226082842
#226082822
#226082802
#226082772
#226082712
#226082632
#226082572
#226082512
#226082432
C2×#179883102
C73×#29242
#1741273